Chapter 10.2, Problem 19E

(a)

To determine

To find: theprobability that all three cards are face cards when eplaced each card before selecting the next card.

Answer to Problem 19E

The answer is: 0.0123.

Explanation of Solution

Given:

a standard deck of 52 playing cards.

Calculation:

Assume, event Abe a face card, event B be a face card and event C be face card. Since, every card is replaced before the next card is chosen, the events are independent.

From information given,

  $P\left(A\right)=P\left(B\right)=P\left(C\right)=\frac{12}{52}$

Therefore, the probability that all three cards are face cards is as follows:

  $\begin{array}{l}P\left(A\text{ and }B\text{ and }C\right)=P\left(A\right)\cdot P\left(B\right)\cdot P\left(C\right)\\ =\frac{12}{52}\cdot \frac{12}{52}\cdot \frac{12}{52}\\ =0.0123\end{array}$

Conclusion:

Therefore, the answer is: 0.0123.

(b)

To determine

To find: the probability of not replacing each card before selecting the next card and compare the probabilities.

Answer to Problem 19E

The answer is: 0.00995.

Explanation of Solution

Calculation:

Assume, event A be a face card, event B be a face card and event C be face card. Since, the card is not replaced before the next card is chosen, the events are dependent.

From information given,

  $P\left(A\right)=P\left(B\right)=P\left(C\right)=\frac{12}{52}$

Therefore, the probability that all three cards are face cards is as follows:

  $\begin{array}{l}P\left(A\text{ and }B\text{ and }C\right)=P\left(A\right)\cdot P\left(B|A\right)\cdot P\left(C|A\text{ and }B\right)\\ =\frac{12}{52}\cdot \frac{11}{51}\cdot \frac{10}{50}\\ =0.00995\end{array}$

Therefore, the answer is: 0.00995.

Conclusion:

Therefore, the answer is: 0.00995.

(c)

To determine

To compare: the probabilities found in part a and part b

Answer to Problem 19E

One is more likely (nearly 1.2 times) to choose face card with replacement.

Explanation of Solution

Calculation:

Divide the larger probability value by the smaller one.

Thus, one is more likely (nearly 1.2 times) to choose face card with replacement.

Conclusion:

Thus, one is more likely (nearly 1.2 times) to choose face card with replacement.